Three-phase air-conditioner compressors are utilized because they have high efficiency. When a single-phase electrical power supply is all that is available for driving such a three-phase compressor, it has been necessary to utilize auxiliary equipment such as starting timers, contactors, and capacitors. Such auxiliary equipment is expensive and adds considerable weight. Single-phase motors heretofore utilized typically are provided with a main winding and a quadrature winding. The quadrature winding has connected to it start and run capacitors. The phase angle of the current in a quadrature winding (lagging the voltage drop in the quadrature winding) due to these capacitors is usually in the range of 60 degrees to 80 degrees lagging but typically can not go beyond 85 degrees lagging. At these small lagging phase angles, a much larger current is required. Also when opening an electrical power switch on a single-phase motor, a high back pressure in some cases can occur, causing the compressor to act like a gas motor and to spin in the backwards direction, with gas flowing from the outlet port to the inlet port. If the motor is re-energized during this state as a single-phase motor, it may continue to run at full speed in the backwards direction, which is very undesirable. To prevent such an occurrence, a reverse-direction lock-out relay is often installed, so that the electrical power can not be applied to the motor when the shaft is running backwards. There is therefore a need for a new and improved apparatus and method for driving a three-phase compressor from a single-phase electrical power supply which overcomes these difficulties.